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Reliability Analysis and Optimisation of Subsea Compression System facing
Operational Covariate Stresses.
Ikenna Anthony Okaro and Longbin Tao*
School of Marine Science and Technology, Newcastle University, Newcastle upon Tyne, NE1
7RU, England, United Kingdom
Keywords: Subsea process system, Subsea control system, Subsea Power System, Reliability
analysis, Weibull Analysis, Risk analysis, Human and Operational factors,
*Corresponding author: [email protected]
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Abstract
This paper proposes an enhanced Weibull-Corrosion Covariate model for reliability assessment of a system facing operational stresses. The newly developed model is applied to a Subsea Gas Compression System planned for offshore West Africa to predict its reliability index. System technical failure was modelled by developing a Weibull failure model incorporating a physically tested corrosion profile as stress in order to quantify the survival rate of the system under additional operational covariates including marine pH, temperature and pressure. Using Reliability Block Diagrams and enhanced Fusell-Vesely formulations, the whole system was systematically decomposed to sub-systems to analyse the criticality of each component and optimize them. Human reliability was addressed using an enhanced barrier weighting method. A rapid degradation curve is obtained on a subsea system relative to the base case subjected to a time-dependent corrosion stress factor. It reveals that subsea system components failed faster than their Mean time to failure specifications from Offshore Reliability Database as a result of cumulative marine stresses exertion. The case study demonstrated that the reliability of a subsea system can be systematically optimized by modelling the system under higher technical and organizational stresses, prioritizing the critical sub-systems and making befitting provisions for redundancy and tolerances.
1.0Introduction
The huge loss and sanctions experienced during the 2010 Macondo oil spill due to the failure
of Subsea Blow-out Preventer, the 2011 Bonga incident and a host of recent offshore failures
has sparked accelerated efforts towards improvement of reliability, risk management and asset
integrity of subsea systems [1][2] [3].
An investigation conducted by the UK Health and Safety Executive [4] indicated that nearly
80% of risk posed to offshore workers emanate from process related failures. These failures
which often cause accidents, downtimes and serious economic losses emanate from the
complex interaction between human and technical factors which cause approximately 70% and
30% of offshore incidents respectively [5].
With an increasing appetite for subsea processing installations , risk exposure could even be
higher due to lack of standardized reliability data and the fact that underwater assets when
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deployed to the marine environment are exposed to additional stresses brought by dynamic
influencing factors of the sea [6][7]. This justifies any study which seeks to understand the
equipment failure behaviour in subsea conditions to ensure maximum uptime. The highly
specialized subsea sector is not exactly known for standardized asset life cycle reliability
procedures [8] because there seems to be is a lope-sided focus on the technical reliability
qualification at manufacturing stages of subsea modules by several scholars; whilst appearing
to neglect lifecycle asset reliability especially during the operational stages where the
intertwine between human, equipment, environment is more pronounced [9].
Although, risks and failure cannot be completely eradicated from any system, they certainly
can be controlled through enhanced reliability strategies throughout the lifecycle of the project.
As the world’s first subsea compression system - a joint industry project is currently underway
at the Asgard field offshore Norway and planned to commence operations in 2015 [10] [11],
major concerns raised by stakeholders bother on reliability, corrosion and production assurance
due to past experiences and losses encountered.
This study presents an enhancement to a concept known as Accelerated Life Testing (ALT);
an analysis procedure whereby basic system failure data is subjected to a high level of
operational stress (covariate) and used to forecast the behaviour of a system [12]. The new
approach which adopts a two-prong methodology for both technical and human reliability
analysis consists of further development of the works of [13]-[16], where remarkable
contributions were made on Weibull-based covariate relationships for technical reliability
analysis and human factor analysis respectively.
Deep water production hardware is exposed to high CO2 pressure and temperature
conditions which directly affect the degradation rate and performance of such materials [17].
At temperatures below 5 and when pressures get much higher than 7.38 MPa, CO2 could be
in its supercritical state. In the absence of water, supercritical CO2 is not corrosive, however,
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under normal deep water production operations, water is always present. When CO2 dissolves
in water, carbonic acid (H2CO3) is formed which significantly increases the corrosion rate of
carbon steels and other materials. The mechanisms of CO2 corrosion under supercritical
conditions do not change compared to those identified at lower partial pressure [18].
The behaviour of a subsea system is better understood from a system reliability viewpoint
[19] which may connote a reliability study on equipment availability times, an asset integrity
assessment, a hazard and operability (HAZOP) study dealing with operability of a system or
even a profitability analysis in terms of production capacity and revenue appraisal. In other
contexts, it could imply Net Present Value (NPV) of a project, economic and management
measures.
At the forefront of reliability analysis techniques is Monte Carlo’s simulation which has
been widely used over decades to quantitatively capture the realistic multi-state dynamics and
stochastic behaviour of components and systems in reasonable computing times [20].
Lund, [21], developed a statistics-based dynamic model for analysing offshore petroleum
projects considering a number of uncertainty factors. The model incorporates several types of
flexibility such as drilling options, uncertainties and capacity expansion uncertainties. A case
study was carried out using the model and it shows that flexibility in capacity improves a
project’s economic value especially when there are many uncertainties surrounding the
offshore reservoir. Unfortunately, considerations for human error estimation were not
considered in the proposition.
Jablownosky et al [22], modelled a subsea reservoir uncertainty and measured the value of
flexibility of assets for various capacities that could be expanded in the future in order to
maximize the project’s net present value. The major deficiency of the proposed model was its
lack of explicit consideration for operational safety in a subsea scenario as it largely focused
on the economic aspect of the oil field. Norris et al [23], incorporated physical parameters into
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risk analysis by coupling laboratory-derived probabilistic nucleation model with existing
deterministic calculations for hydrate growth.
The works of Lin, [24] and Lin [25] suggested flexibility models for deep water oil field
systems which were simulated using Monte Carlo’s model to determine the value of specified
flexibilities under the uncertainty conditions of reservoir and production capacity [24] [25].
The models did not address the severity of influence on CAPEX and OPEX contrary to Lee et
al [26] wherein a design procedure for offshore installations Life cycle Cost Analysis under
various environmental load stresses was presented.
System failure data is usually gathered from historical performance archives, but in practice,
these data are insufficient and are not always available to reflect the real operational conditions
of its purposed domain [27].
In further attempts to account for these operational life conditions, a number of numerical
models consisting of life-covariate relationship such as the Arrhenius model, Proportional
Hazard model (PHM), Eyring model Extended Hazard Regression, Inverse Power Law had
been seen to provide acceptable results [12]. Reliability analysis had been carried out using
experimentally or field-sourced sourced failure data and applying predictive models in order
to extrapolate results of system reliability beyond the given data range [28]-[35]. For example,
in PHM, the operational conditions are considered to be a covariate such that the reliability of
the system is a product of time and covariates. The covariate acts multiplicatively on the
threshold hazard rate by some constant [14].
The major limitation of life covariate models such as PHM is that they usually has many
assumptions which are not applicable in many real world cases. It can only be applied to time-
independent covariates; notwithstanding, it is still the most frequently used due to its simplicity
and commercial application [15].
In a bid to enforce reliability practice across the subsea industry, ISO 20815 standard stressed
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the need for representation of stochastic variations related to lifetimes and restoration times
using probability distributions while AP1 17N RP provided a structured approach which
organisations can adopt for management of uncertainty throughout project lifecycle [36].
Modelling complications are encountered when process variables such as temperatures, mass
flows, pressures, affects the probability of occurrence of the events in resonance with human
and organisational influence, thus the evolution of a subsequent scenario [23] [45].
Accelerated life testing (ALT) reliability analysis is meant to help operators ascertain the
difference between the reliability warranty values suggested by the manufactures and the
realistic asset performance [34] being that risk influencing factors such as seabed temperature
of 5 at 4000 meters of depth, PCO2 fugacity, and pH which are prevalent and are major
agents of asset degradation at seabed. Ideally, real historical failure data are the most suitable
for reliability modelling. Unfortunately, such data only become available towards the end life
of a system and this justifies the use of OREDA values for MTTF in place of real field data.
OREDA is a unique data source of mean failure rates, failure mode distribution and repair
times for equipment used in the offshore industry from a wide variety of geographic areas,
installations, equipment types and generic operating conditions [45].
MTTF is the mean of the distribution of a product’s life calculated by dividing the total
operating time accumulated by a defined a group of devices within a given period of time by
the total number of failures in that time period. This is based on a statistical sample and is not
intended to predict a specific unit’s reliability, in order words, MTTF is not a necessarily
warranty statement but manufacturer’s statistical prediction devoid of usage environment
variations.
The model proposed in this paper was developed under the principle of time series prediction
of basic failure rate with an external stress is known as accelerated failure testing (AFT).In
AFT, the covariates act multiplicatively with the failure time by some constant and the aim is
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to accelerate or decelerate failure time. This assumption provides a physical or chemical
interpretation for the effect of covariates on the failure time. Hence, the AFT can be more
appealing in many cases due to this direct interpretation [24]. Furthermore, unlike proportional
hazards models, regression parameter estimates from AFT models are robust to omitted
covariates, and they can be used to quantify the effect of time-dependent covariates.
One of the most important applications of AFT is the analyses of failure data whereby collected
data is subjected to on high level of operational stress (covariate) is used to predict the
behaviour of a system [12][28][30][34].
The analysis of ALT data consists of (i) selection of an underlying life distribution that
describes the system and Weibull analysis (ii) incorporating a life-covariate relationship
development.
The aim is to solve the problem of unplanned failure of oil and gas equipment during
production system operation in subsea environments because OREDA data only considers
individual failure time of each component without the knowledge and information on the
interaction among the components and with external forces lead to failure. The methodology
features a combination of the statistical confidence bounds of a two parameter Weibull model
and a covariate model to create a new reliability model technical failure assessment.
The main contribution of the present study is the proposition of a new parametric method
for predicting failure times, improving the uptime and reliability of an equipment- a subsea gas
compression system in this case; by parametrizing a Weibull model so that it becomes an
Accelerated Failure Testing Model such that a covariate stress vector which is made up of
temperature, pressure, pH is applied to the entire system so that critical failure components are
identified and optimized. It is an important issue since unplanned failure of a subsea oil and
gas production system could result in significant economic loss, safety risk, fatality or even
sanctions.
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2.0 Methodology
In the proposed reliability analysis model, it is assumed that subsea equipment or systems
installed in the marine environment are subject to corrosion-induced degradation and human
factor impact. A Weibull hazard rate relationship is derived and merged with a corrosion profile
expression to produce the new reliability assessment model. Human and operation reliability
are also evaluated using a barrier analysis method. Reliability analysis starts from definition of
targets; however, actual quantitative assessment involves the following distinct tasks.
Derive formulations for selected reliability assessment method.
Calculate the basic scale and shape parameter of the failure data.
Determine the Corrosion profile and Corrosion Weibull Reliability Index.
Decompose system using Reliability Block Diagram and evaluate failure frequencies.
Optimize system by analysing Fusell-Vesely reliability importance of components
based on failure frequencies and achievable reliability.
Evaluate human-factor reliability using Barrier and Operational Analysis (BORA)
method.
The flow chart in Fig 1 shows the process of reliability analysis adopted for this work
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Fig 1: Flowchart of Reliability Assessment Process.
2.1 Mathematical Formulation of Weibull Hazard Rate Model.
The basic Weibull model assumes that the family of the equation has two parameters where
a basic failure rate of a distribution can be expressed as [13].
(1)
Wherein the constant α represents the scale parameter which is often termed the characteristic
life of a system because it rates the time variable t with constant β representing the slope of the
distribution as it determines the shape of the rate function.
The principle implies that if β is greater than one, the rate function increases with t, whereas if
β is less than 1 then the rate function decreases with t. When β = 1, the rate function is constant
and assumes an exponential distribution.
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Stochastically, the first failure can happen before the expected number of failures reaches 1,
thus the need to select an appropriate benchmark time between failures.
Given a population of n components, with each possessing the same failure density f(t), the
probability for each individual component failing by time F(tm ) is
(2)
Denoting the failure probability value by , the probability that certainly j components failed
and (n− j ) did not fail at time tm is
; 1 (3)
It then follows the Median Rank which is the probability of j components or more failing at the
time tm is given by
0304
(4)
This is also known as the median rank formula.
On deriving the natural log of the two sides and negating we get
ln
1
1
(5)
Then taking the natural log again, we have
ln ln
1
1ln ln
(6)
To illustrate the equations, assume a population of n has 100 components (at time t = 0),
which has been in continuous operation. Assuming the first failure occurs at a time t = t1, then
the estimated number of failures at the time of the first failure equals 1 [13]. This means that
F(t 1) = N(t1)/n = 1/100.
As an extension to the basic Weibull model, a regression analysis on failure data proposed
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by [38] gives model parameters of shape (β), scale (α) and intercept (b) which are used to
estimate the hazard rate. The hazard or survival rate of an item is a measure of the probability
of an item to fail at about a specific time t, in the presence of a covariate factor c, provided it
has been available up to time t [39]
Hence the hazard rate considering the covariate factor c, is defined as [38]
, lim
∆ →
∆ | ,∆
(7)
If t represents time to failure. Then the hazard rate can be expressed as
, (8)
where cα = c1α1 + c1α1…. crαr, and α is the regression coefficient of the corresponding r
covariates. It then follows that when 1, the covariate factor c = 0 and Equation (8)
will give the hazard rate So(t) [40].
The function can represent a wide range of functions, although it is considered an
exponential function made up of product of the regression coefficient and the covariate.
Since the reliability assumes a Weibull distribution, the hazard rate in the presence of covariate
can be expressed as
,
(9)
where λ and β are scale and shape parameters in the order laid out.
If / , the hazard rate can be rewritten as
(10)
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,
2.2 Model Formulation of the Weibull Corrosion-Covariate Stressor
The corrosion covariate profile entails physical parameters such as marine pH, temperature
and CO2 pressure which are the key forces that affect an asset wear-out curve based on
corrosion. The effects of corrosion whether external, internal or uniform are widely known to
cause wear, fatigue and leakage. The extrapolation of regression analysis results beyond
available data range requires accurate, justified, and tested covariate-life models [34][40]. To
model the system in full water-wet condition, the Norsok’s Corrosion profile model was
adopted and merged with the developed Weibull hazard expression guided by the principle of
Arrhenius reaction model for accelerated life reliability analysis.
The Norsok corrosion model was chosen as the covariate factor because an increase in the
CO2 partial pressure usually results in a drastic increase in the corrosion rate, a behaviour that
is enhanced with temperature and causes the major degradation (failure) of both steel and non-
steel units of the subsea compression system. It is a reliable physical relation developed, tested
and proven to represent the oxidizing and corrosive impact of physical factors such as (CO2)
partial pressure, temperature and flow [41].
The corrosion profile relationship for a deep water asset located in a zone with temperature
5 can be estimated using;
. (11)
where KT = Temperature Constant
FCO2 = Fugacity of CO2 pressure
F = Fugacity of pH
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The Arrhenius asset life model is governed by the principle that life of a system is directly
proportional to the inverse reaction rate. The Arrhenius equation is given by [40].
(12)
L signifies a quantifiable life measure while V stands for the covariate factor, developed for
thermal-corrosion related variables in absolute units. C and b represent model parameters
which can be calculated from analysis of variance of data.
If scale parameter is regarded as a function of the covariate, then hazard rate, h becomes,
,
(13)
Since temperature profile could give a life measure, it also makes sense for a corrosion
profile stress to be part of the life covariate functions. On substituting the corrosion profile
variable v into the survivability equation, system hazard rate under the influence of corrosive
stress becomes,
,
(14)
Reliability can thus be expressed as,
,
(15)
Reliability can also be expressed as a function of
1 (16)
2.3 Decomposition with Reliability Block Diagram (RBD) and Optimisation
Reliability analysis with block diagrams is an evaluation method which is important when
technical faults are being traced to its roots in a complex system (Fig 2). It is used to represent
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the complex connections and reliability interactions of the system’s components.
Fig 2: A typical system with both series and parallel relationships.
2.4 Reliability Optimisation
To develop an optimisation model, consider a system with x amount of components and the
target is to optimize reliability to meet reliability without over-designing certain components
to the detriment of other critical ones to minimise cost.
The optimality factor is the ratio of targeted reliability index for a system and its weibull-
corrosion covariate reliability index multiplied by the failure time or basic Mean Time to Failure
(MTTF) of a system.
Mathematically, Optimality factor (OF) is,
(17)
The reliability importance ( ) of a system is defined as the ratio of system reliability
to minimum reliability value ( ). It refers to the criticality a certain component exerts on
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overall reliability. Mathematically, Reliability Importance (IR) is expressed as [42].
(18)
The Benchmark Minimum Failure (Minimum MTTF) can also be estimated and this refers
to the product of the optimality factor and the reliability importance of a component. It is an
expression that is used to arbitrarily extract resources from the over-designed components and
evenly add to the under-designed or early failure ones. Two assumptions are made when
evaluating the minimum time to failure.
An assumption that if a component’s life expectancy is more than three standard
deviations beyond the statistical control limits (especially if beyond upper control
limits) of the unstressed failure distribution, then the excess life would be extracted
from the over-designed component and evenly shared among less reliable components
within a sub-system.
If the reliability importance of a component is 0 or less than 0.1, the minimum time to
failure remains the same as unstressed failure data. (See table 5 )
Optimal Time to Failure (Optimal MTTF) is gotten by dividing-up the extracted life values
obtained from over-designed among other components, thereby optimizing and extending its
life to failure.
2.5 Human-factor Analysis.
Several investigations into offshore mishaps show that technical, human, operational as well
enterprise-wide factors contribute to accidents. Despite all these, many works on quantitative
risk analysis of subsea system focus just on the technical reliability of the systems thereby
neglecting the influence from humans [43]. Several models have been propounded for Human
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reliability analysis. These include, methods such as Technique for Human Error Rate
Prediction – THERP, Human Error Assessment and Reduction Technique – HEART, Success
Likelihood Index Method Multi-attribute Utility Decomposition – SLIM-MAUD and more
recent techniques which are often referred to as second generation, or advanced methods such
as Cognitive Reliability and Error Analysis Method – CREAM, Standardized Plant Analysis
Risk Human Reliability Analysis – SPAR-H, Information, Decision and Action in Crew
context – IDAC, in addition to probabilistic ones such as Bayesians models [2][3] ,
Organisational Risk Influence Model- ORIM, Model of Accident Causation using Hierarchical
Influence Network-MACHINE. The major challenge is that many of these models with the
exception of [2][3] were not particularly designed with reference to offshore risk inputs and
industry average occurrence rate of those accidents[16][55].
The method employed for human factor analysis in the paper is a simplification of the
Barrier and Operational Risk Analysis (BORA) model by [16] which is a very comprehensive
framework for modelling and optimising barriers on offshore production installations. The
introduction of severity measure in this paper is a major enhancement of the BORA
methodology because it readily compares and presents the monetary consequence of impeding
system risk. Industry average probability was decided by calculating the mean of participant’s
rating for each category. The status of these factors for the specific oil field was also obtained
in the same manner.
A Risk Influencing Factor (RIF) template was designed to collect rate and code human
factor data. It comprises of five categories of human factor risks which relate to Personnel
factors, Task factors, Technical elements, Administrative and Operational Philosophy. No
special root cause event was modelled in this work; rather a generic exposure to human factor
risk was quantified alongside the severity implication across the whole system. The technical
element will embed the stressed reliability index that is generated from the initial Weibull
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corrosion covariate expression.
In line with BORA recommended approach, the formula for calculating the revised Risk
Influencing factor P(rev) is given by [16] [43].
∑
(19)
where Pave (X) represents the industry average of probability of occurrence of an event X,
Wi is the weight allocation of the Risk influencing factor and Qi represents an actual measure
of the status of Risk influencing factor at field. The severity of the Risk Influencing Factor
(RIF) is ranked on a scale of A to E with A (representing outstanding practice in Industry) to
E (Worst practice in industry) where C corresponds to industry average. Table 1 summarises
all the input data, rating system and weights applied to the risk influencing factor and the
adjustment ratio.
Table 1: Risk Factor Code Table
The modification factor (MF) depends on the product of allocated weights (Wi) and rated
event probability (Qi).
(20)
The weights are applied relative to the importance of each factor on scales 0.2, 0.4, 0.6, 0.8
Risk Factor Rank (Q) Code for Risk Factor (Q.Code) Meaning Revised Probability (Prev)
A 1 Good performance 0.00-0.15B 2 Best Practice 0.16-0.25C 3 Industry Average 0.26-0.35D 4 Below Industry Average 0.36-0.45E 5 Bad Practice 0.46 - 1.00
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and 1.0; where 0.2 means the least importance/influence and 1.0 meaning the utmost
importance. Event probability (Q) is rated using a scale of A-E as shown in Table 1. The true
value for the technical reliability index obtained from the new model is weighted together with
the interview data obtained from survey for all factors in each category.
3. Case Study
The purpose of this case study is to demonstrate the applicability of the new model
developed in Section 3 for reliability analysis and optimisation of a subsea compression system.
3. 1 Description of the case
A major oil and gas firm wants to conduct a reliability assurance analysis on a subsea gas
compression system proposed for the installation at the Escravos field off the coast of Nigeria,
West Africa. The target reliability is 95% for the initial 300 days. To support decision making
processes, the firm had requested for a numeric quantity of the subsea system’s survivability
under operational stresses. The system which is directly synchronized with power units, a
process system and control system is meant to take reservoir gas from the wellhead, through
the compression system to a centrally positioned FPSO. The compression unit performs the
mechanical job of compressing well fluid while the power units provide electric power for the
entire system. The control system conveys and receives sensor signals between the Subsea
Engineers on deck.
3.2 Case Analysis -Weibull-Corrosion Covariate Reliability Analysis
The MTTF column of each component of the subsea compression system in table 2 seems
to readily show the failure times however it is imperative to carry out a more detailed analysis
to determine the systems contribution or insufficiencies towards 95% reliability target at a
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certain defined time. Majority of the failure data were obtained from OREDA [54]. Prior to
the regression analysis of the MTTF data, some adjustments were performed to make the
distribution a Weibull distribution. Firstly, the failure data is ranked in descending order as
shown in the column ‘Rank’ of Table 2. The median rank for failure is then calculated to
ascertain the proportion of the system component that will fail by the mean time in column
MTTF.
Using the Bernard’s equation for determining median rank [13]:
0.30.4
(21)
where X represents the column rank and N is the sum of failed components being considered .
In this case, there are 39 components as shown in Table 2.
The median rank and MTTF are further transformed by taking their natural logs using Eq.
5 and repeated with equation 6; so that regression analysis can take place more efficiently. A
simple linear regression analysis is performed between ‘In MTTF’ and ln(ln(1/(1-Median
Rank) in order to obtain parameter estimates in determining the survival rate.
Table 2: Derivation of Natural logs of component failure time (t) and Median Ranks
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The scale parameter and the shape parameter are obtained from linear regression analysis [47]
of In(In(1-Median Rank)) and In MTTF columns in table 2 above. The coefficients obtained
are 473.36, 0.47 and the intercept -2.9.
The Weibull scale parameter (α) was obtained by substituting the b and β in Equation (22).
(22)
In line with Weibull’s principles, the characteristic life indicates the time at which 63%
of system components would have failed irrespective of the value of [12][13]. With an
assumption that MTTF is expressed in days, the results from regression analysis indicate that
at 473.36 (days), the unstressed reliability of the system in the absence of any repair or
replacement work would be 37%.
No SUBSEA COMPRESSION SYSTEM MTTFSOURCE Rank Rank1Median Rank 1/(1-Median Rank ln(ln(1/(1-Median Rank)) ln(MTTF) Process System
1 Manifold Piping 3,048 OREDA 5.6 1 0.017766497 1.018087855 -4.021491042 1.72276662 Mechanical Connector 1,351 OREDA 6.1 2 0.043147208 1.045092838 -3.121165758 1.808288773 ROV Isolation Valve 1,389 OREDA 6.3 3 0.068527919 1.073569482 -2.645229481 1.840549634 EI Isolation Valve/Actuator 1,489 OREDA 7 4 0.093908629 1.103641457 -2.316530606 1.945910155 Check Valve 162 OREDA 8.1 5 0.11928934 1.135446686 -2.063362471 2.091864066 Scrubber 50 OREDA 9 6 0.144670051 1.169139466 -1.856182932 2.140066167 Scrubber Level Detector 98 Tracerco 24.5 7 0.170050761 1.204892966 -1.679910065 3.198673128 Magnetic Bearing System Compressor 27 S2M Report 27 8 0.195431472 1.242902208 -1.525790316 3.30688679 Compressor 9 OREDA 32 9 0.220812183 1.283387622 -1.388283692 3.4657359
10 Electric Motor(Compressor) 5.6 Aker Solution 38.7 10 0.246192893 1.326599327 -1.26365639 3.655839611 PSD Sensors 124 OREDA 41 11 0.271573604 1.3728223 -1.149267807 3.7135720712 Flow Meter for Anti Surge Control 650 OREDA 43 12 0.296954315 1.422382671 -1.043177384 3.7612001213 Anti Surge Actuator 228 Aker Solution 50 13 0.322335025 1.475655431 -0.943913114 3.9120230114 Anti Surge Valve 89 OREDA 70 14 0.347715736 1.53307393 -0.850327856 4.2484952415 Cooler 84 OREDA 84 15 0.373096447 1.5951417 -0.761506169 4.430816816 Condensate Pump Unit 6.1 KOP 89 16 0.398477157 1.662447257 -0.676701617 4.4886363717 Re-circulation choke valve 32 OREDA 89 17 0.423857868 1.735682819 -0.595293163 4.4886363718 Meg Piping 309 OREDA 98 18 0.449238579 1.815668203 -0.516753902 4.5849674819 Pressure and Volume Controller 89 OREDA 100 19 0.474619289 1.903381643 -0.440627964 4.60517019
Control System20 Top Side Master Control Station 24.5 OREDA 108 20 0.5 2 -0.366512921 4.6821312321 Wet Mate Connector 24980 OREDA 124 21 0.525380711 2.106951872 -0.294045889 4.8202815722 Electrical Dry Mate Connector 4424 OREDA 162 22 0.550761421 2.225988701 -0.222892112 5.0875963423 Electric Jumpers 72022 Teledyne 192 23 0.576142132 2.359281437 -0.152735069 5.2574953724 Junction Boxes 41 Telecordia 228 24 0.601522843 2.50955414 -0.083267372 5.4293456325 Magnetic Bearing Control Module 6.3 S2M Report 309 25 0.626903553 2.680272109 -0.014181765 5.7333412826 Anti-Surge Compressor Control Pod 38.7 CFD DOC 310 26 0.652284264 2.875912409 0.054838487 5.736572327 SCM 43 OREDA 358 27 0.677664975 3.102362205 0.124130689 5.8805329928 UPS 8.1 OREDA 554 28 0.703045685 3.367521368 0.19406646 6.31716469
Power System29 Topside Main Circuit Breaker 1116 OREDA 554 29 0.728426396 3.682242991 0.265069889 6.3171646930 Topside Transformers 554 Vetco Gray 650 30 0.753807107 4.06185567 0.33764293 6.4769723631 VSD 7 OREDA 675 31 0.779187817 4.528735632 0.412402847 6.5147126932 Topside Umbilical Hang-off 358 OREDA 1116 32 0.804568528 5.116883117 0.490140445 7.0175061433 Power Umbilical 108 OREDA 1,351 33 0.829949239 5.880597015 0.571915995 7.2086003434 Umbilical Termination Assembly(UTA) 310 OREDA 1,389 34 0.855329949 6.912280702 0.659228202 7.2363393435 Subsea Enclosures (Transformer) 675 OREDA 1,489 35 0.88071066 8.382978723 0.754337905 7.3058600336 Subsea Main StepDown Transformer 554 Vetco Gray 3,048 36 0.906091371 10.64864865 0.86096109 8.0222409237 Hv Penetrator/Dry Connector 192 Deutch 4424 37 0.931472081 14.59259259 0.986008583 8.3947995438 Hv Power Jumper 100 OREDA 24980 38 0.956852792 23.17647059 1.145221526 10.125830839 Hv Wet Mate Connector 70 Deutch 72022 39 0.982233503 56.28571429 1.39387574 11.1847269
21
To check the fitness of Weibull 2-parameter modelling for analysis, a line fit plot as shown in
Fig 3 between failure values and the natural log of the median is generated.
Fig 3: Line Fit plot showing fitness of data for reliability analysis
On close observation of fig 3, the fitted line has little doglegs which show that the failure
modes affecting the system come from various origins [46]. In the current case, these can be
overlooked because such scatter plot is typical for the hydro-mechanical components. The
OREDA failure data being used generates such shape parameter of the failure distribution as
supported by [46][47] provided that the straight line slope of such plot gives the shape
parameter of the distribution. The plot has shown that the Weibull distribution modelling is a
good choice and the generated values fit properly with theoretical values.
The reliability of the subsea compression components under the influence of external
operational stress was evaluated by applying a thermal-corrosion profile stressor since the basic
Weibull reliability analysis only predicted cumulative failure times without due consideration
22
of the external influential forces that could interfere and further reduce system reliability.
Values of the boundary variables were obtained from experts at the Egina field Nigeria. The
temperature profile for West African waters is shown in Fig 4.
Fig 4: Temperature Profile for a West African Offshore Field [48]
The corrosion profile, for the subsea compression system was obtained using (reference of the
following equation):
. (23)
If the water depth 1500 meters, Temperature Constant at 5 degrees Celsius KT = 0.42 [41];
FCO2 = Fugacity of CO2 pressure = 5840psi = 40265kPa (Field data);
F = Fugacity of pH at West African Water at pH 9 = 0.2208 (Field data)
Therefore, 11.8
Having generated a covariate parameter to represent the influence of marine conditions, next
step is to estimate the overall reliability index of the SCS system using Equation 15 as shown
below containing the values of the shape and scale parameters derived from the failure data:
,
2.9.
473
.
(24)
2015105
2500
2000
1500
1000
500
0
Temperature (Celsius)
Wat
er D
epth
(M
eter
s)
Temperature Profile for Offshore West Africa
23
A stressed survival signature has been proven to be an effective method to estimate the
survival function of systems with multiple component [42] and table 3 shows the values for
both stressed and unstressed failure data using the new failure model. The contribution to
unreliability by each failure data is taken into account and as a consequence, bounds of survival
functions of the system and ratings of relative importance index values can be obtained using
further optimization analysis.
Table 3: Reliability Table for Basic Weibull Failure and Stressed Failure.
24
Fig 5: Basic Weibull failure vs Stressed Weibull-Corrosion failure.
The result in Table 3 and Fig 5 show the impact of marine physical conditions on failure rate.
The asset-life decline curve obtained from the stressed Weibull-covariate model gave a steeper
decline curve compared to the unstressed Weibull failure model. This result further confirms
that a catastrophic infant mortality is imminent if the quality and redundancy configurations of
the components are not improved.
3.3 Root-Cause Analysis using Reliability Block Diagram.
Boolean algebra expressions defined by the MTTFs data of each component from table 2
are used to determine minimal cut sets or the minimum combination of failures required to
cause a system failure. The RBD calculates system failure frequency and unavailability based
on the Vesely model. The fundamental law guiding the analysis using ITEM software used for
the RBD decomposition is the Weibull failure distribution principle and an extrapolation of
failure data by the Vesely theory [49].The rationale guiding the combination of both laws is
the assumption that there are no repairs thus failure is assumed as an exponential degradation
300250200150100500
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Time (days)
Rel
iabi
lity
Inde
x Unstressed FailureWeibull-Corrosion Model Stressed
Variable
25
curve. All failures are statistically independent. The failure rate of each subsea component is
constant. After repair, the system will be as good as old, not as good as new based on the
Weibull distribution model being applied. All component failures are statistically independent.
The failure rate of reach equipment item is constant. The repair rate for each equipment item
is constant. After repair, the system will be as good as new, (i.e., the repaired component is
returned to the same initial state, with the same failure characteristics that it would have had if
the failure had not occurred; repair is not considered to be a renewal process [49].
Let component failure rate be,
1 (25)
1 (26)
(27)
/ (28)
Where represents time specific unreliability of the system, is the time specific
recovery frequency of the system , time-specific failure frequency of the system, is
the time specific failure rate of the system, the time specific recovery rate of the system, K
is the phase of minimal cut set and t is time. More detailed derivation can be found in Jincheng
[49].
The Fusell-Vesely measurement highlights an event’s contribution to system unavailability
because it gives an idea on the likelihood that a component is down because a system is down.
It is very important to identify those components in a system which have the greatest impact
on overall system reliability. In practice, this is done by first choosing a suitable measure
of component importance, calculating them for each component and then ranking the
importance of components according to that measure. In this paper, a presentation is made
of the various results for the power, process and control systems. This can be used to
compare the relative importance of system components by calculating their Fussell–Vesely
26
importance measures so that the components can be ordered by their structural criticality.
These results help to quickly estimate optimizable components, because calculating the
exact values of the component importance measures is very laborious in a large and
complex system [50].
The RBD analysis was based on an enhanced Vesely theory which allowed the allocation
of reliability capabilities to each block based on the logical failure of the system with respect
to series and parallel connections. Fundamentally, the RBDs offer a higher probability of
dangerous failure than other advanced techniques [19]. In this study, it was applied to model
and decompose the system failures into cut-sets in order to visualize how the system is set-up
and measure the actual faulty components so that a good logic for their optimization analysis
will suffice rather than using a generic fault tree which is more suitable for sensitivity analysis
without optimization details. It should be noted that it was used in a different way in the present
analysis to consider the cut-sets on a node by node basis of process, control and power sub-
systems. The clear advantage is that it simply allows the software’s failure estimation rule to
analyse the contribution of each component to unreliability.
To trace the key contributors to unreliability, the system is unbundled into its components
parts using parallel and series connections as obtainable in its instrumentation diagram (Fig 6).
27
Fig 6: Reliability Block Diagram of the Subsea Compression System
3.3.1 Reliability Analysis of the Process Sub-System
The process sub-system is the section of the subsea compression plant where actual
separation well fluid and compression of gas occurs. An RBD diagram of the process sub-
system is cut out from the main subsea compression system and calibrated accordingly with
the MTTF values of Table 2. A simulation is run using ITEM Reliability Software for a lifetime
of 7200 hours or 300 days and an average MTTR of 7 applied to each component. The
component failure data is fed to the system. 100 iterations are run on each sub-system as
obtained from Piping and instrumentation drawings to determine the severity index and
reliability importance of the components. This iteration is repeated for all the sub-systems.
The failure severity index measures the intensity of unreliability of each sub-system
The Failure Severity index is mathematically expressed as
x x (29)
Where T represents Time, represents Failure frequency and represents Expected failures.
The aim of the procedure is to capture the key components that contribute to unreliability
28
and their various reliability importance for adequate system optimization. Fig 7 shows the
reliability blocks configuration into a mix of series and parallel cut-sets as obtainable in
realistic configuration.
Fig 7: Reliability Block Diagram (RBD) of SCS Process Sub-System
The reliability index of the process system was found to be 0. This implies that the system
is completely unreliable. The failure frequency was 12.3% and the total number of expected
failures was 88.5. The risk severity factor using equation (29) is 170 which seems moderate
but does not count as reliable because the failure frequency of other critical components meant
the entire Sub-System has an infant premature failure.
29
Fig 8: Time vs Unreliability for Process Sub-System
The time and unreliability index graph shown in Fig 8 indicates that the unreliability of the
process components rapidly increases and attains full unreliability value in 288 days which
significantly deviates from the target benchmark of 300 days or 7200 hours. The reliability of
this system in relation to target operation benchmark is zero, therefore, all the critical
components need to be optimized.
16001400120010008006004002000
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Mean Time Step
Unr
elia
bilit
y In
dex
(%)
30
Fig 9: Reliability Importance for Process Sub-system Components Systems.
Figure 9 shows the reliability importance chart of process components. To identify the
critical components which need reliability upgrade the most, another analysis is subsequently
run using Fusell-Vesely’s equation (FV). Fussell-Vesely Importance of the modelled plant
feature (usually a component, train, or system) is defined as the fractional decrease in total risk
level (usually CDF) when the plant feature is assumed perfectly reliable (failure rate = 0.0). If
all the sequences comprising the total risk level (e.g. CDF) are minimal, the F-V also equals
the fractional contribution to the total risk level of all sequences containing the (failed) feature
of interest. Where F-V = 1-1/RRW and RRW is Risk Reduction Worth (RRW) [51].
Change in unavailability of events with high importance values will have the most significant
effect on system unavailability.
∑
(31)
Fig 9 above shows that the Meg Piping with zero reliability importance index, Mechanical
MEG
MechC
onnec
tor;
ROVIso
Valve;
FMSurg
eContr
ol;
PVContro
ller;
AntiSu
rge;
Check
Valve;
Condensa
tePum
p;
PSDSe
nsor;
E lectri
cMoto
r;
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Process Components
Ves
ely
Rel
iabi
lity
Impo
rtan
ce (
%)
31
connector and Isolation Valve contributes least to unreliability while the electric motor with an
importance factor of 68%, the PSD Sensor and condensate pump are top contributors to
frequent failure of the process sub-system. A trade-off on cost will then guide the choice of
redundancy or quality improvement to be made on the components.
3.3.2 Analysis of the Control Sub-system.
The control sub-system entails the auto-sensory segment which continuously monitors the
overall condition of the subsea compression plant. In (Fig 10), the system is wired-up in
reliability configuration and reliability analysis simulation is run through on the cut-sets.
Fig 10: Reliability Block Diagram (RBD) of the Control Sub-System.
The reliability index of the control sub-system was found to be 0 with 498 failures and 4180
total downtimes. This implies that the control sub-system is completely unreliable. Using
ITEM software, the failure frequency was found to be 0.0685 and the total number of expected
failures was 88.5. The risk severity factor was found to be 170 which appears relatively average
but ironically does not impact positively on overall reliability since the failure frequency of
other critical components meant the entire sub-system has an infant failure rate.
32
Fig 11: Time vs Unreliability of the Control Sub-System
The control system chart in Fig 11 appears to be the main contributor to failure being that
complete unreliability was reached within 72 days. The system fails rather earlier than the
benchmark target therefore a further investigation to identify the contributors is justified. Recall
some components in this sub-system has the highest MTTF with Wet Mate Connector and
Electric Jumpers having 24980 and 72022 MTTFs respectively according to table 2. This
analysis reveals that a high MTTF does not directly translate to high reliability rather the
cumulative MTTFs together with frequency and times of failure gives better prediction of
system reliability.
4003002001000
1.0
0.8
0.6
0.4
0.2
0.0
Mean Time Step
Unr
elia
bilit
y In
dex
(%)
33
Fig 12: Reliability Importance for the Control Sub-system.
Fig 12 shows that the Subsea Control Module (SCM) and the Dry Connector did not
contribute much to unreliability rather it the Master Control and UPS that are critically
important to overall system reliability because they contribute to unreliability by 32% and 68%
respectively.
This implies that a significant upgrade of these two components will significantly improve the
reliability of the control system cut set.
SCM
MBControlM
od,
Juncti
onBoxe
s,
AntiSu
rgeCo
ntrol,
Electr
i cJum
pers,
WetM
ateCo
nnecto
r,
DryCone
ctor,
MasterC
ontrol,
UPS,
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Control System Components
Ves
ely
Rel
iabi
lity
Impo
rtan
ce
34
3.3.3 Analysis of the Power Sub-System
The power system supplies the electric voltage that runs the subsea compression system. It is
an integral part of the system that runs from the top side through the umbilical cable down to
the base of the ocean where the compressor is located. Arhenius Law and Basquin Law posited
that electronic components fail due to an increased ambient temperature [52]. It is possible to
extend the life of the power components beyond the mean MTTF using pressure protective
enclosures for the power sub-components as demonstrated by [53], however this particular
research seeks to identify how the system configuration contributes to reliability and failure
severity for stochastic optimisation. This implies that temperature fluctuations underwater have
serious impact on the lifespan of the power sub-components. To account for this, the model
law assumes a uniform fatality constant for stress based on the Weibull reliability index earlier
estimated in 3.2. Fig 13 below shows that the decomposition and of power system in series
connection based on instrumentation diagrams obtained for the case study.
Fig 13: Reliability Block Diagram (RBD) of the Power Sub-System
Based on the RBD Fuselly-Vesely of the power system in Fig 13, the reliability index of the
power sub-system was found to be 82% with 0.086 failures. The power sub-system was found
35
to be the most reliable and of least reliability importance. The failure frequency was 0.167%
for the sum of total number of expected failures was 0.176. The severity index was found to be
0.002 disregarding the fact that it had 11 cut-sets.
Fig 14: Time Vs Unreliability of the Power Sub-system
The power sub-system is the least contributor to failure of the whole subsea compression
system being almost 99.9% of reliability was maintained further in time step than other sub-
systems. Fig 14 shows that, at maximal unreliability, the system maintains a total unreliability
of 0.18 in 1 time step. System unreliability is relatively low and varies almost linearly with
time. The three data points on Fig 14 established a sufficient convincing trend, however, in real
field applications; curve fitting may be exercised on the graph to determine the best-fit decision
for reliability improvement.
1.00.80.60.40.20.0
0.20
0.15
0.10
0.05
0.00
Time Step
Unr
elia
bilit
y
36
Fig 15: Reliability Importance of the Power Sub-system
The Variable Speed Drive (VSD) was identified as the critical item to be improved in the power
segment. The high voltage connector may also need to be optimized, because, under subsea
operational circumstances, the failure rate would increase. Table 4 shows a break-down of the
results from sub-systems reliability assessment. Table 4 showcases the severity table of the
whole system based on the Weibull analysis and Fusell-Vesely of the minimal cut sets. Minimal
cut sets depend on the number of blocks in connection in each sub-system. A two-tailed F-test
reveals that there is no relationship between the number of cut sets and expected failure,
reliability, unreliability and failure frequency but there seems to be relationship between
number of cut sets and severity. Thus, the lower the cut sets, the higher the severity. The biggest
contributor to severity factor is total downtime.
TCirc
uitBreak
er
Subse
aTran
sform
er
TopTra
nsfo
rmer
UmbilicalT
ermAss
y
HVDryC
onnec
tor
PowerU
mbili cal
HVPowerJ
umper
HVWetC
onnecto
rVSD
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Power Components
Ves
ely
Rel
iabi
lity
Impo
rtan
ce
37
Table 4: Summary Table of Sub-Systems Reliability
3.4 Optimisation of the Subsea Compression System
Optimisation of the whole Subsea Compression System requires a careful consideration of the
Weibull-Corrosion Covariate results of table (3) and table (4).
Since basic Weibull analysis has showed an infant mortality failure, it is imperative that the
design is optimized to achieve the necessary reliability levels. Based on the requirement of
96% reliability at 300 days, a close look at the system components’ MTTF indicates that that
up to 25 components were under-designed while 14 were over-designed. The low survivability
of majority of the individual components was responsible for the low value of β and the
subsequent stress induced failure.
An optimisation of the lope-sided reliability design can be achieved by enhanced process
control at the design stage and subsequent identification of reliability importance of the
various components. Fig 16 shows the process control chart of the system.
Subsea Compression Sub-Systems No of Cut Sets Unreliability (%) Reliability (%) Total Downtime Expected Failures Failure Frequency SeverityProcess System 19 1 0 156.64 88.5 0.0123 170.51Control System 9 1 0 4180 496 0.0685 142019.68Power System 11 0.17 0.823 0.086 0.176 0.1617 0.002
38
Fig 16: Statistical Process Control Chart for Design Optimisation
System optimization using control charts helps to identify design needs from a cumulative
perspective. In Fig 16, it can be observed that the design violated the seven-point rule which
suggests that seven consecutive data points above or below the mean indicates a problem with
the process. With a mean MTTF of 2945 as benchmark, a standard deviation of the mean (CL)
2945 gives an upper control limit (UCL) and a lower control limit (LCL) of 39703 and -33182
respectively. There is then room for process-smoothing and possibly cost balancing as these
will help to prevent the discrepancy resulted from either over-design or poor designs. Whole
failure time of any components that falls out of the standard limits would need to have some of
its value extracted and shared out to deficient components in the distribution. This further
confirms that unavailability of the subsea compression system under review is due to poor
design and process control of individual components therefore there is a need for further
analysis of the sub-systems and components to trace the key contributors to unreliability.
403020100
80000
60000
40000
20000
0
-20000
-40000
Equipment Number
Tim
e to
Fai
lure
MTTF DATACLUCLLCL
Variable
39
Table 5: Optimized Subsea Compression System
Table 5 shows the optimisation of the subsea compression system to maintain 96% reliability
at 300 days. The RBD decomposition of the entire system into its constituent components and
analysis with pre-set algorithms in the ITEM software helped to analyse the contribution of
each component to overall reliability. Whilst some components needed an increase MTTF,
others for instance No (13), (Electric Jumpers) had way too much uptime life and its optimal
MTTF had to be smoothened to a lower value to accommodate other deficient components.
The components whose reliability importance are 0 or less than 0.1 are left untouched as seen
in No (1), (Manifold Piping) in Table 5 where 3048 was both the initial MTTF and minimum
MTTF but only increased to 3877 by taking a percentage of the extracted excess life of the
No SUBSEA COMPRESSION SYSTEM Initial MTTF Optimality Factor Reliability Importance Minimum MTTF Optimal MTTF Process System
1 Manifold Piping 3,048 58,522 0 3,048 3,877
2 Mechanical Connector 1,351 25,939 0 1,351 2,180
3 ROV Isolation Valve 1,389 26,669 0.04 1066.752 1,895
4 EI Isolation Valve/Actuator 1,489 28,589 0 1,489 2,318
5 Check Valve 162 3,110 0.25 777.6 1,606
6 Scrubber 50 960 0.12 115.2 944
7 Scrubber Level Detector 98 1,882 0.56 1053.696 1,882
8 Magnetic Bearing System Compressor 27 518 0.32 165.888 995
9 Compressor 9 173 0.43 74.304 903
10 Electric Motor(Compressor) 5.6 108 0.69 74.1888 903
11 PSD Sensors 124 2,381 0.44 1047.552 1,876
12 Flow Meter for Anti Surge Control 650 12,480 0.08 998.4 1,827
13 Anti Surge Actuator 228 4,378 0.18 787.968 1,617
14 Anti Surge Valve 89 1,709 0.44 751.872 1,581
15 Cooler 84 1,613 0.08 129.024 958
16 Condensate Pump Unit 6.1 117 0.44 51.5328 880
17 Re-circulation choke valve 32 614 0.22 135.168 964
18 Meg Piping 309 5,933 0 309 1,138
19 Pressure and Volume Controller 89 1,709 0.11 187.968 1,017
Control System20 Top Side Master Control Station 24.5 470 0.32 150.528 979
21 Wet Mate Connector 24980 479,616 0 24980 25,809
22 Electrical Dry Mate Connector 4424 84,941 0 4424 5,253
23 Electric Jumpers 72022 1,382,822 0 39703 39,703
24 Junction Boxes 41 787 0 41 870
25 Magnetic Bearing Control Module 6.3 121 0 6.3 835
26 Anti-Surge Compressor Control Pod 38.7 743 0 38.7 867
27 SCM 43 826 0 43 872
28 UPS 8.1 156 0.67 104.1984 933
Power System29 Topside Main Circuit Breaker 1116 21,427 0 1116 1,945
30 Topside Transformers 554 10,637 0 554 1,383
31 VSD 7 134 0.72 96.768 925
32 Topside Umbilical Hang-off 358 6,874 0 358 1,187
33 Power Umbilical 108 2,074 0 108 937
34 Umbilical Termination Assembly(UTA) 310 5,952 0 310 1,139
35 Subsea Enclosures (Transformer) 675 12,960 0 675 1,504
36 Subsea Main StepDown Transformer 554 10,637 0 554 1,383
37 Hv Penetrator/Dry Connector 192 3,686 0.02 192 1,021
38 Hv Power Jumper 100 1,920 0.05 100 929
39 Hv Wet Mate Connector 70 1,344 0.08 70 899
40
Electric Jumpers.
3.5 Human-Factor Reliability Assessment
A questionnaire based on the Delphi method was developed by interviewing experts from the
West African subsea sector. The questionnaire was reviewed by a reference panel to confirm
its academic and ethical status. The panel was made up of engineering experts whose
backgrounds were operation, maintenance, and subsea engineering.
A pilot survey was launched and little adjustments were effected on the final draft before the
proper interview was carried out. The first section of the interview was designed to discover
the company’s main business activities, experience and technical know-how of the respondents
and in order to understand how the operations are shared-out within the company while at the
second section, the company’s subsea personnel were required to highlight its strategy for
offshore system maintenance activities and the operational challenges at play. Their opinions
were measured on a scale and the same questionnaire was used in order to maintain uniformity
of data from participants.
Five key factors were analysed being that they are factors during the installation, production
and maintenance stages of a typical West African oil field. Ten specialists were interviewed
through phone calls. Five of the specialists work with operators, two specialists work with
subsea manufacturing companies and the other two specialists work with a company providing
subsea consultancy service.
Each of the specialists possess a minimum four years’ experience with subsea systems and at
least 10 years’ experience in several engineering and management positions within the subsea
oil and gas industry. Based on the respondents’ profiles, the study reasonably indicated current
trends and rating regarding human factor and operation indices of subsea oil and gas production
practices, problems and issues in the installation.
For this case, the reliability value derived from the Weibull-Covariate analysis performed was
41
fed to the slot for the technical condition/reliability system and the severity code read-off. The
revised probability of failure in Tables 5 and 6 show that the most contributing Risk Influencing
Factor (RIF) is personnel factors with a 56% probability of failure and the overall least RIF is
technical factors with a 29% probability of occurrence. The severity index could be transcribed
into weighted financial consequences from depending on pre-set benchmarks. From the results,
urgent effort needs to be made towards smart resource allocation and staff scheduling in order
to reduce human fatigue risks, improve occupational health and safety, and associated cost
implications. Whilst the sum of Revised Probability (Prev) of Influence for the technical RIFs
seem to be relatively low due, a look at the modification factor shows that elements such as
material properties and process complexity of the system were both significantly high at 1.2,
thus, requires improvement. Table 6 entails an enhanced method for human reliability
assessment for quantitatively assessing the risk in a particular scenario.
42
Table 6: Human Reliability Analysis Table
Table 7: Risk Matrix Table of the RIFs
No RISK INFLUENCE FACTOR
Industry Average (Pave)
Weight (W)
Risk Influencing Factor (Q)
Code for Risk Influencing Factor (Q. Code)
Moderation Factor (MF)
Average Moderation Factor (MF Ave.)
Revised Probability (Prev)
1 PERSONNEL FACTORS 0.45 1.25 0.56251a Competence 0.8 C 3 2.41b Work Stress 0.2 D 2 0.41c Fatigue Rate 0.2 D 2 0.41d Health Condition 0.6 C 3 1.8
2 TASK FACTORS 0.44 1.01 0.44632a Ergonomics 0.5 C 3 1.52b Supervision 0.2 C 3 0.62c Methodology 0.4 D 2 0.82d Time Pressure 0.8 E 1 0.82e Sufficient Work Tools 0.2 D 2 0.42f Spares Availability 0.2 C 3 0.62d Explosivity/Inflamability 0.8 C 3 2.4
3 TECHNICAL ELEMENTS 0.37 0.77 0.28543a Equipment Design 0.2 C 3 0.63b Material Properties 0.4 C 3 1.23c Process Complexity 0.4 C 3 1.23d Human Machine Interface 0.2 D 2 0.44d Maintainability 0.2 D 2 0.45e System Feedback 0.4 D 2 0.85f Technical Condition/Reliability 0.8 E 1 0.8
4 ADMINISTRATIVE 0.33 1 0.334a Work Permit 0.2 C 3 0.64b Work Safety Analysis 0.4 C 3 1.24c Procedures/Protocols 0.4 C 3 1.2
5 OPERATIONAL PHILOSOPHY 0.35 1.16 0.4065a Trainings 0.6 C 3 1.85b Enterprise Feedback Loops 0.4 D 2 0.85c Communication 0.6 C 3 1.85d Regulation 0.4 D 2 0.85e Management of Changes 0.2 C 3 0.6
RATING
10 20 30 40 50 60
i Personnel Factorii Task Factoriii Techanical Elementsiv Administrative
v Operational Philosophy
Severity Index(Percentage)
Risk Factor
43
3.6 Strengths and Limitations
The key contribution of the research is a new systematic methodology for stressing a
low-stress failure data such as OREDA MTTF in order to predict a realistic failure
curve and optimize an asset which has little field records but bound to face exponential
covariate vectors of operational stresses afield.
To model the reliability of a system in full water-wet condition, the Norsok’s Corrosion
profile model was adopted and incorporated with the newly developed Weibull failure
expression by implementing the principle of Arrhenius reaction model for accelerated
life reliability analysis.
The motivation of the current study is due to the unavailability of any known
publication which addresses the reliability and optimization of a Subsea Gas
Compression System - an emerging technology that had only been launched in 2015 at
Asgard field, Norway.
Further development of the present reliability analysis method shows that the baseline
reliability index of a system were stressed with statistical stress based on intended
operating environment, in this case corrosion profile considering extended parameters
such as subsea temperature, pressure, pH and fugacity variables, so that weak
components are identified and an optimal MTTF is proposed (either increased, kept
constant or decreased) for each component as shown in Table 5.
The reliability analysis conducted in this study focused on an enhanced reliability model
developed for the subsea compression system. A model is a simplified representation of the
true system, and for practical reasons, it cannot describe all features of the system with 100%
accuracy. For instance, the inaccuracies may relate to, the configuration of the system and the
production capacities of the system for various equipment states. Some degree of subjectivity
might have affected the weights and responses received from the interviewees on human
reliability. However, the strength of the overall reliability assessment model lies in its ability
44
to visualize the life failure data, accelerate failure life and project optimal tolerances for subsea
equipment subjected to operational influences of both the marine and human factors. The
corrosion-Weibull covariate model produced valid benchmark which is vital for the
improvement of the overall design of the subsea compression system for longer life.
Redundancies and back-up systems were not considered in this study however, the detailed
statistical analysis of the system has a 95% confidence status.
4. Conclusion
This paper constitutes a step forward in the use of advanced qualitative and quantitative
analysis for assessing the reliability of the emerging subsea compression system.
This paper reveals that a high MTTF component does not directly translate to high
reliability of a system rather the cumulative MTTFs together with frequency and times
of failure gives better prediction of system reliability.
It is more efficient and time-saving to (a) identify any infant mortality (b) identify over-
designed components by applying Weibull failure model and Fusell-Vesely theory to
their minimal cut sets for optimizing overall reliability index based on criticality and
reliability importance of components. The initial basic reliability of the system was
optimized by a margin of 52% from 0.45 to 0.95 based on the confidence interval of
the whole reliability analysis.
The analysis indicate that there is no significant relationship between the number of
cut sets and expected failure, reliability, unreliability and failure frequency but there
seems to be relationship between number of cut sets and severity. Thus, the lower the
cut sets, the higher the severity risk. However, the biggest contributor to severity factor
is total downtime.
45
The operational requirements of a subsea gas compression system can be understood
and optimized by embedding a high operational stressor using a covariate corrosion
profile on a weibull model of component failure distribution, then reliability
decomposition of the sub-components to identify the critical components and an
optimization analysis based on reliability importance of each sub-component.
Low subsea temperatures, high Co2 fugacity and pH variation has a significant impact
on asset degradation rate, failure modes and frequency over a time series. Personnel
factors such as competence of the operators, works stress, fatigue, stress, and
ergonomics constitute the highest weight of risk influencing factors that could cause a
subsea gas compression system – based on the geographical setting of the study.
The new model demonstrated a significant originality in producing more realistic
failure rate compared to the basic reliability models which does not consider credible
external influences.
The newly developed method in the paper combines the powerful calculative abilities of a
Weibull with corrosion covariate model together with systematic decomposition of the whole
system with RBD analysis, subsequent identification of the reliability importance of each
component and the novel optimisation method therein.
Using well-known physical based life-covariate supported by systematic operational survey
and optimisation through RBD decomposition, the model provides a suitable statistical
approach for achieving in-depth knowledge on inherent risks towards a system and
optimization. Future work may consider additional stress covariates and make an in-depth
focus on the relationship between the cut sets and unreliability, failure frequency and failure
times.
46
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Abbreviations
Abbreviation Meaning
API American Petroleum Institute
BP/D Barrels Per Day
BORA Barrier and Operational Risk Analysis
CAPEX Capital Expenditure
DNV Det Norske Veritas
FTA Fault Tree Analysis
FMECA Failure Mode Effects and Criticality Analysis
HSE Health and Safety
ISO International Standards Organisation
MTTF Mean Time to Failure
OPEX Operation Expenditure
P/A Per Annum
UK United Kingdom